k-means clustering.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euclidian_distance(point_0, point_1):\n",
    "    distance = (point_0[0] - point_1[0]) ** 2 + (point_0[1] - point_1[1]) ** 2\n",
    "    return np.sqrt(distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'y': [47, 20, 28, 86, 67, 77, 64, 73, 21, 83, 8, 4, 3, 69, 65, 66, 65, 42, 86, 16, 21, 80, 77, 50, 8, 59, 52, 33, 78, 1, 26, 58, 1, 96, 90, 12, 53, 59, 71, 42, 50, 45, 2, 42, 43, 64, 85, 95, 54, 85, 25, 54, 54, 86, 44, 9, 7, 77, 84, 68, 14, 94, 53, 35, 46, 8, 58, 30, 78, 80, 93, 90, 22, 69, 60, 3, 64, 1, 55, 80, 90, 58, 27, 2, 85, 14, 32, 62, 10, 93, 96, 62, 27, 74, 88, 95, 13, 47, 96, 28], 'x': [4, 21, 12, 33, 8, 79, 34, 69, 95, 61, 16, 48, 27, 18, 23, 22, 75, 5, 2, 5, 24, 46, 65, 52, 68, 43, 44, 20, 86, 63, 46, 93, 41, 56, 47, 38, 6, 26, 56, 9, 64, 39, 69, 70, 23, 83, 35, 94, 60, 48, 44, 22, 8, 55, 70, 52, 42, 68, 30, 1, 96, 65, 14, 23, 12, 75, 18, 61, 30, 75, 26, 45, 19, 31, 46, 37, 76, 8, 50, 18, 78, 67, 70, 80, 30, 18, 24, 66, 43, 57, 51, 25, 35, 89, 22, 68, 7, 71, 12, 9]}\n"
     ]
    }
   ],
   "source": [
    "data_points = {\n",
    "    \"x\":[],\n",
    "    \"y\":[]\n",
    "}\n",
    "data_points_count = 100\n",
    "\n",
    "for i in range(data_points_count):\n",
    "    point_x = np.random.randint(1, 99)\n",
    "    point_y = np.random.randint(1, 99)\n",
    "    data_points[\"x\"].append(point_x )\n",
    "    data_points[\"y\"].append(point_y )\n",
    "\n",
    "print(data_points)\n",
    "assert len(data_points[\"x\"]) == len(data_points[\"y\"])\n",
    "\n",
    "centroids_count = 3\n",
    "centroids = {\n",
    "    \"x\":[],\n",
    "    \"y\":[]\n",
    "}\n",
    "\n",
    "colors = [\"y\", \"g\", \"r\"]\n",
    "\n",
    "assert len(colors) == centroids_count\n",
    "for i in range(centroids_count):\n",
    "    centroids[\"x\"].append(point_x)\n",
    "    centroids[\"y\"].append(point_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 100)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f473ae9b080>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(centroids_count):\n",
    "    plt.scatter(centroids[\"x\"][i], centroids[\"y\"][i], color=colors[i])\n",
    "i = 0\n",
    "plt.scatter(centroids[\"x\"][i], centroids[\"y\"][i], color=colors[i])\n",
    "plt.scatter(data_points['x'], data_points['y'], color='k')\n",
    "plt.xlim(0, 100)\n",
    "plt.ylim(0, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[9, 28], [9, 28], [9, 28]]\n"
     ]
    }
   ],
   "source": [
    "centroids_position = []\n",
    "for i in range(centroids_count):\n",
    "    centroids_position.append([centroids[\"x\"][i], centroids[\"y\"][i]])\n",
    "print(centroids_position)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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qdLXnZXe/sEwi2ErnMKHPM2PhAACiABaUxEBtBIsPD7k+rTS153R/mNFbwVU+KWG5o8QQAARQOugQACtBAuPDzUDOMBc+u2/Utsf01Y4hQ95mh8JAQQQAbSmIgJoJVh4POvTCk+AQM0P/UMjULM4DQRaE0AAEcDWyVMFIoBWgsSfexOIQ8GekSREFwRCLjXoov6UCQHfBBBABNCaUwiglSDxZwiUvj6NNOiWADOA3fKl9PQIIIAIoDVrEUArQeLPESh1fRop0D0Blhp0z5gzpEUAAUQArRmLAFoJEg8BCAQhwFY4QTBzkkQIIIAIoDVVEUArQeIhAIFgBFhqEAw1J4qcAAKIAFpTFAG0EiQeAhAISoClBkFxc7JICSCACKA1NRFAK0HiIQABCEAAAoEJIIB5C+C0pNdK+iVJPyjpVknvlPQGt9tGlWtTkl4n6XmSLpX0EUkvkvSlmrmIANYE1eYwZiraUCszhlwps999tZr88UUynXIQwLwF8NWSXibpOZI+K+nHJd0o6TWS3lql6SskvUrSNZK+Iun1kh4q6cGSvlMjlRHAGpDaHMI7S9tQKzOGXCmz3321mvzxRTKtchDAvAXwbyTdJulXhtLyJknfrmYF3eyfmxV8i6Q3V8dcUsU4IXxPjXRGAGtAanrI4GnF4U2RXRlTU67LpNXVVS0uLjYtluMzJECuZNipAZtE/gSEHdmpEMC8BdDNAD5f0hMlfVHSwyX9fTUr+BeS7ifpy5IeIelTQ7n5oervyzXyFQGsAanJIbyztAmtso8lV8ruf2vryR8rwbTjEcC8BfBukt4o6bcknZbk1gS627+/W6Xt1dWavyskbQ2l8nurNYLPHJPeF0lyfwafiyVtnDp1Svv2ORfkYyXAGwusBMuJJ1fK6esuWkr+dEE1nTIRwLwF8FmS/kDSy6s1gD8qaaWaAXyXpN0E8H2VMLr40Y97qOS60f+IAPob9Lyz1B/L3EsiV3Lv4W7bR/50yzf20hHAvAXwFklvkvRHQ4l4bbX+74EtbwEzA9jxqOZXeceAMyqeXMmoM3toCvnTA/SITokA5i2A/ynJCd87hnLOPfH7XEn3d88UVA+BuAdA3IMg7uPu436jeiqYh0B6GKwlv7OUrSiaJVzJudKMFEePI1BK/nBdGZ//CGDeAuj2/HuCpBdUt4Ddwx5/IunPJLntX9zH/e8rq61i1qttYB7GNjD9fmGU+M5StqJol3Ml5ko7UkSNI5B7/nBd2T3vEcC8BdA9oOH29XuapB+oZvuOSvodSXdVaTHYCNo9Lew2gv6wpBdXTw3XuWLyFHAdSi2OKemdpWxF0SJBhkJKyhUbKaJ3k8Dl5WVtbGyc++e5uTmtrKwkvd0U15W98x0BzFsAQ1ztEMAOKZdw64KtKPwkUAm54ocUpex2O/jEiRPa2trSzMyM5ufnNT3tNo5I88N1ZXK/IYAI4OQs2fsIBNBKsPB4FqIXngCJN98i3pbY2LH13TauK5MzBAFEACdnCQJoZUT8HgTYioL0SJWAZX2ZJTZ2XjG0jevK5CxBABHAyVmCAFoZEb8HAX6pkx4pErCsL7PExs4qlrZxXZmcKQggAjg5SxBAKyPi9yBQylYUJEE+BCzryyyxsROMqW1cVyZnCwKIAE7OEgTQyoj4CQRy34qCBMiLgGV2yRIbO8XY2sZ1Ze+MQQARQOs1hYdArASJP0OArUxIhFQIWNaXWWJj5xNj27iu7J41CCACaL2mIIBWgsSfI9D3k4N0BQTqELDMdFli69Stz2NibRvXlfFZgQAigNbrBQJoJUg8BCCQFAHL+jJLbOyQcm5b7Ozb1A8BRADb5M1wDAJoJUg8BCCQHAHL+jJLbOygcm5b7Oyb1g8BRACb5szo8QiglSDxEIBAkgQs68sssbHDyrltsbNvUj8EEAFski/jjkUArQSJhwAEkiVgWV9miY0dWM5ti5193fohgAhg3VzZ7TgE0EqQeAhAAAIQiI5A7hKLACKA1kGHAFoJEg+BFAicPi2dOCFtbUkzM9L8vDQ9nULNqSMEGhOI4XV2jSvdMAABRAAbpsyOwxFAK0HiIRA7gWPHpOVlaWPjfE1nZ6XDh6XFxdhrT/0g0IhALK+za1TpFgcjgAhgi7S5IAQBtBIkHgIxE3Dyt7QkbW9fWMupqbN/X11FAj32X+63HT2i6qSomF5n10kDhwpFABFAa44hgFaCxEMgVgLutu/+/RfO/A3X1UmgmwlcX+d2sIc+LOG2owdMnRYR62bWXTQaAUQArXmFAFoJEg+BWAkcPy4dODC5dmtr0sLC5OM4YlcCpdx2jD0FYnydXVfMEEAE0JpbCKCVIPEQiJXA0aPSoUOTa3fkiHTw4OTjOGIsgZJuO8aeAswAxt5DfutXLWTxW2hBpSGABXU2TS2MADOAQTq8JOkIAtRwkpJeZ8cMIDOAhqFyJhQBtBIkHgKxEhisAdzc3PkQiKszawC99FxJtx29AOu4kFJeZ4cAIoDWoYQAWgkSD4GYCQyeAnZ1HH4SmKeAvfUaM4DeUHorqITX2SGACKB1wCCAVoLEQyB2AuP2AZybk1ZW2ALGQ9+VdNvRA65gReS+JQ8CiABaBxMCaCVIPARSIBDoTSC5f+nu1tWl3HZMIdVLqSMCiABacx0BtBIkHgIQOEOg9H3wSrjtSKrHQwABRACt2YgAWgkSDwEInJG/paUlbY+8cWSqWmu4urqqxQJeO1fqDChDIDwBBBABtGYdAmglSDwECifAPniFJwDN74UAAogAWhMPAbQSJB4ChRPgKdjCE4Dm90IAAUQArYmHAFoJEg+BwgmwD17hCUDzeyGAACKA1sRDAK0EiYdA4QSYASw8AWh+LwQQQATQmngIoJXgHvEsCJdg0GGCRVI0++BF0hFUoygCCCACaE14BNBKcJf40rfEcFhg0FFyRVgs++BF2ClUKWsCCCACaE1wBNBKcEw8W2KclT+2BekguSIukn3wIu4cqpYdAQQQAbQmNQJoJTgSz5YYZ2/77t+/XxsbG2Ppur3hZmdntb6+runpac89QHF9EuCWf5/0OXdJBBBABNCa7xcIIBdvK06JBfEwsGcRJUAAAhDYmwACiABax8g5Abz55pu1vLx8wayNm6U5fPhwETv4W0EO4tkSQ4KBr2yiHAhAAALjCSCACKB1bJwRwD//8z/Xs5/97OJf42SF6eKZAYSBjzyiDAhAAAJ7EUAAEUDrCDkjgFdccYVuvfXWsWWxXqsZYrbEOL8GcHNzc8ePCkeTnGqWUxwNAQhAYJQAAogAWkfFGQGsU8ja2poWFhbqHOrlmJTXI7IlxvmngF0ybG9vn8sJJ3/us7q6ytICLyOFQiAAgRIJIIAIoDXvawvgkSNHdPDgQev5asXnsH8cW2KM3wdwbm5OKysryF+tkcBBEIAABMYTQAARQOvYqC2AoWYAc9o/LuVZTGtiDeJh4Isk5UAAAhA4TwABRACt4+HcGsCtra3e12uxf9ze3YlMWdOdeAhAAAJ5EEAAEUBrJl/wFLArrM/1WjxBu3t35nBb3JqsxEMAAhCAwFkCCCACaB0Le+4DGHq9FvvHje/OnG6LWxOWeAhAAAIQQABdDpx9pJBPWwJRvQmEGcCd3cht8bapTRwEIACBfAkwA4gAWrM7qncBs4fezu6sK8XXXnutfvqnf1rz8/O8X9c6KoiHQGIEWB+cWId5qC4CiABa0ygqAXSNYQ+9C7u07m3xQRSv77MOCeIhkBYB1gen1V++aosAIoDWXIpOAAcSOPpe4tDrEa1gfcXXnQEcnI+Nln2RpxwIxE+A9cHx91FXNUQAEUBrbkUpgK5R3NI427WTbouPSwBetWYdFsRDIH4CrA+Ov4+6rCECiABa8ytaAbQ2LKf43W6LT2pjqM27J9Wj7b/zI6AtOeJKIFD37kAM64MZy/4zEgFEAK1ZhQBaCQaKH7fOZ9KpQ76+b1Jdmv4765qaEuP40giksj6YsdxNZiKACKA1sxBAK8GA8YNf0R/84Af1hje8YeKZU50BZF3TxK7lAAio7gzgAFUf64MZy90lKgKIAFqzCwG0EuwhftK6wJTXALKuqYeE4pRJEph0HRjXqJDXBsZyt2mFACKA1gxDAK0Ee4rPdbucurMaqc5u9pQunDZTAjGvD2Ysd5t0CCACaM0wBNBKsMf4cWtrUt8up+66ppTXN/aYMpw6QwKxrg9mLHebbAggAmjNMATQSrDn+NyermPWoOeE4vRJEohxfTBjudtUQgARQGuGIYBWgonEpyKKk9Y1hVzDlEjXUk3PBFIZK+OaHdP4iakunlMkiuIQQATQmogIoJVgAvGpbcOQ6/rGBFKl+CqmNlbGdVhM4yemuuSW3AggAmjNaQTQSjDy+FS3YchxfWPkqVJ89VIdK7tJYCyv02QsdzO0EEAE0JpZCKCVYMTxqW/DkPKtuIjTgqqNIZD6WNntdvCJEye0tbWlmZkZzc/Pa3p6upf+Zyz7x44AIoDWrEIArQQjjmcRdsSdQ9WiIsBYiao7qEwNAgggAlgjTfY8BAG0Eow4nm0YIu4cqhYVAcZKVN1BZWoQQAARwBppggBaIaUaz6xGqj1HvUMTYKyEJs75rAQQQATQmkPMAFoJRhzPNgwRd85I1Vgj1W9fMVb65c/ZmxNAAPMXwPtK+j1JT5Z0L0knJT1X0serdJmS9DpJz5N0qaSPSHqRpC/VTCcEsCaoVA9jG4b4ey6HrUfipzy5hoyVyYw4Ih4CCGDeAniZpE9KWpP0Dkm3S/phSV+u/rhMfIWkV0m6RtJXJL1e0kMlPVjSd2qkKgJYA1Lqh7ANQ7w9mNPWI/FSrl8zxkp9VhzZLwEEMG8BfJOkx0qa3yXN3OzfrZLeIunN1TGXSLqtEsL31EhPBLAGpBwO4RZjfL2Y49Yj8VFuXiPGSnNmRIQngADmLYCfk/QBSbOSHi9pU9LbJf1plWr3q2YCHyHpU0Pp96Hq78tjUvIiSe7P4HOxpI1Tp05p3z7ngnxKIsAXnd/ebsqTBw/88qc0CJREAAHMWwAHt3D/UNL7JP2EpBVJL5D0bklXV2v+rpC0NZT475W0LemZYwbDayVdN/rfEcCSLhtn28q6M7993oYnW4/47QNKg0BJBBDAvAXwruphDyd6g89bJT1S0mP2EEAni6clPYsZwJIuB/Xbyrqz+qzqHNmWJzOAdehyDAQgMI4AApi3AH5V0j9I+tWhzndP+F4ryT0d3OYW8GgesQawsGsL6878driFJ1uP+O0LSoNASQQQwLwF8IikuZGHQK6X9Khq9m/wEIh7AMQ9COI+Tui+wUMgcVwGmq4JC1FrZp38UrbyZOsRv/3RVWkxjuWu2kq54wnElgMIYN4C6G71/lO1Zs+t63NrAN0DIM+X9BdVirptYF4p6TmS1qttYB7GNjD9X8LarAkLUWvWnfml7IMnW4/47RPfpcU6ln23k/J2JxBjDiCAeQugy8aflfS71f5/TvDcAyGDp4Ddvw82gnZS6DaC/rCkF0v6Ys3BzC3gmqCaHNZ2TViTc7Q91jpj1fa8ucb54hnb7EKu/dW0XTGP5aZt4fh2BGLNAQQwfwFsl7H1oxDA+qxqHWlZE1brBMaDWHdmBDgSDk+/PGMqLfaxHBOrXOsScw4ggAigddwhgFaCI/G+ZoQ8V+uC4lh35pcuPP3yjKW0FMZyLKxyrUfMOYAAIoDWcYcAWgmOxPtYE+a5SmOLY92ZX8rw9MszhtJSGcsxsMq1DjHnAAKIAFrHHQJoJZjgDOCgyqw789v58PTLs+/SYp796ZtNKeePOQcQQATQOg4RQCvBkXjWhHkGSnEQ6IkAY7kn8BGdNuYcQAARQOtQQQCtBMfEsyasA6gUCYEeCDCWe4Ae2SljzQEEEAG0DhUE0Epwl3jWhHUElmIhEJgAYzkw8AhPF2MOIIAIoHWoIIBWgnvEsyasQ7gUDYGABBjLAWFHeqrYcgABRACtQwUBtBIkHgIREojtyypCRFQJAkkTQMLHRUMAACAASURBVAARQGsCI4BWgsRDIDICMb62KjJEVAcCyRNAABFAaxIjgFaCxEMgIgKxvrYqIkRUBQJZEEAAEUBrIiOAVoLEQyASAjG/tioSRFQDAtkQQAARQGsyRyuArGHa2bUwsaZ73vExb1rbljw535YccbkTQAARQGuORymArGHa2a0wsaZ6/vExv7aqDX1yvg01YkohgAAigNZcj04AWcM0Xv6Wlpa0vb19wT9OTU2d+fvq6qoWFxetuUB84gRymgHkOpB4MlL9zgkggAigNcmCC+Bet3T6XsMU4+2mvplYE4z4cARifm1VEwrkfBNaHFsqAQQQAbTmflABnHRLp88ZjEl1s4JuG98nk7Z1Jq4/ArG+tqoJEXK+CS2OLZUAAogAWnM/mADWuaXz3e9+V4cOHZrYpiNHjujgwYMTj6t7QJ269XWLNbd1XXX7hOPaE4jxtVVNWkPON6HFsaUSQAARQGvuBxHAurd0brzxRj3hCU+Y2Ka1tTUtLCxMPK7OAXXrtr6+runp6TpFej2G2RCvOIspLMblDHXhk/N1SXFcyQQQQATQmv9BBLDuBf3mm2/WNddco83NzR0PPLiGuoceZmdn5VPG6tbNp3Q26bRc1nU1aXNOx6YsYn31AznfF3nOmxIBBBABtOZrEAFsckvnoosuknvi1X2Gn3rt6onXJnXzedu5ScflsK6rSXtzOTbWdaUp8CXnU+gl6tgnAQQQAbTmXxABbDrLFnINU9O6WYG3jQ/JpG0diTtPIOZ1pan0EzmfSk9Rzz4IIIAIoDXvgghgm1s6oW6dtambFXrb+FBM2taPuLMEYl9XmlI/kfMp9RZ1DUkAAUQArfkWRABdJWO+pRNz3awdTHx4AqnMKocnwxkhAAFfBBBABNCaS8EEcCCBy8vL2tjYOFfvubk5rays9P4mC243WVOJ+AGBFNaV0lsQgEDaBBBABNCawUEFcHB77MSJE9ra2tLMzIzm5+d72V5lHDhuN1nTiXhHgBlA8gACEOiaAAKIAFpzLLgAWitMPARiJ8C60jh7iB94cfYLtWpHAAFEANtlzvkoBNBKkHgIjCGQwrrSkrapKamtDMgyCCCACKA10xFAK0HiIbALgZjXlZa0TU1JbWUwlkMAAUQArdmOAFoJEg+BPQjEeNuxpG1qSmorA7EsAgggAmjNeATQSpB4CCRGoKSHVEpqa2JpSHWNBBBABNCYQkIArQSJh0BiBErapqaktiaWhlTXSAABRACNKYQAWgESD4HUCJQ0K1ZSW1PLQ+prI4AAIoC2DBICaAVIPARSI5DSNjVWtiW11cqK+LQIIIAIoDVjuQVsJUg8BBIkkMI2Nb6wltRWX8woJ34CCCACaM1SBNBKkHgIJEog5m1qfCMtqa2+2VFenAQQQATQmpkIoJUg8RBImECM29R0hbOktnbFkHLjIYAAIoDWbPQmgFxcrV1BPAQgUAoBrpel9HR37UQAEUBrdnkRQF6zZO0G4iEAgVIIcL0spae7bScCiABaM8wsgLxmydoFxEMAAqUQ4HpZSk93304EEAG0ZplJAHnNkhU/8RCAQCkEuF6W0tNh2okAIoDWTDMJYEqbrLLmxpoqxEMAAhYCKV0vLe0kNgwBBBABtGaaSQBTec0Sa26saUI8BCBgJZDK9dLaTuLDEEAAEUBrppkEMIVftKy5saYI8RCAgA8CKVwvfbSTMsIQQAARQGummQQw9tcssebGmh7EQwACvgjEfr301U7KCUMAAUQArZlmEkB38phfs8Qvbmt65B3PutC8+zfG1sV8vYyRF3XanQACiABax4dZAAcSuLy8rI2NjXP1mZub08rKihYXF611bB3PmpvW6LIPZF1o9l0cbQN5LV20XZNUxRBABNCasF4E0FUixtkUZgCt6ZFnPOtC8+zXlFoV4/UyJX7UVUIAEUDrOPAmgNaKdBHPmpsuqKZdJutC0+4/ag8BCJwlgAAigNaxkLUADm5PLy0tneG0vb19jtfU1NSZ/7+6utrrbWprBxLfjACzws14cbSdALN9doaUsJMAAogAWsdF9gI4kMAY1yhaO4/45gRYF9qcGRHtCbDWtD07IvcmgAAigNYxUoQAOkj8CremSh7xzADm0Y8ptIK1pin0Urp1RAARQGv2FiOAVlCxxiO2zXqGdaHNeHF0OwKsNW3Hjaj6BBBABLB+tow/EgG0EuwxnttL7eCzF1s7bkTVJ8BMc31WHNmOAAKIALbLnPNRCKCVYE/x3F6ygWcvNhs/ovcmwFpTMqRrAgggAmjNMQTQSrCHeG4v+YHO7XM/HCllJwFmAMmKrgkggAigNcc6FUDfX7C+y7PC6yueL5e+yHNeCNQjwFrTepw4qj0BBBABbJ89ZyM7E0Df69N8l2cF12c8t5f6pM+5IVCPgLtm/eIv/uKuB990003sQVoPJUeNIYAAIoDWgdGJAPpen+a7PCu0vuOZAey7Bzg/BCYTQAAnM+KI9gQQQASwffZ0NAPoe32a7/KswGKI5/ZSDL1AHSCwOwGuW2RH1wQQQATQmmPeZwB9z075Ls8KLJZ4tjKJpSeoBwR2EuC6RVZ0TQABRACtOeZdAH2vT/NdnhVYTPFsZRJTb1AXCJwnwHWLbOiaAAKIAFpzzLsA+v7l67s8K7DY4nkyOrYeoT4QkLhukQVdE0AAEUBrjnkXQN/r03yXZwVGPAQgAIFJBLhuTSLEv1sJIIDlCOCrJL1R0mFJv1klzj0lvUXSsyRdJOkDkl4s6bYGieVdAN25fa9P811eAz4cCgEIQKAVAa5brbARVJMAAliGAD5S0nsl3SlpbUgA3yHpqZKukXRK0g2SvifpsTXzxx3WiQAOJHB5eVkbGxvnqjM3N6eVlZVWe1+x3q1Br3IoBCAQBQGuW1F0Q5aVQADzF8Dvl/SJambvWkmfqgTwEkm3SzokabXK7gdK+rykx0j6aM2M70wA3fl9r0/zXV5NRhwGAQhAoDUBrlut0RG4BwEEMH8BfJekOyS9VNLxIQH8KUkflHSZpG8O5chXJa1Iun6XvHG3it2fwediSRunTp3Svn3OBflAAAIQgAAEIBA7AQQwbwF0a/teI8ndAv7OiAC6mb8bR2TO5eu/VLeJX7FL8r5W0nWj/4YAxj7UqR8EIAABCEDgPAEEMF8BnJP0cUlPlPTpqsuHZwB3E8CPVTODr2QGkEsFBCAAAQhAIE8CCGC+AvgLkv7SLaMbSt1pSdvVgx4/I+nmFreAR0dCp2sA8xx2tAoCEIAABCDQLwEEMF8BdGvzfmgkvdwt33+X9HuSbqkeAjko6abquPtL+kJMD4H0Ozw4OwQgAAEIQCBPAghgvgI4LmOHbwG7f3fbwDyl2gbGbRHztiro6gbpzgxgA1gcCgEIQAACEIiBAAJYtgAONoJ2s4DDG0F/vUFyIoANYHEoBCAAAQhAIAYCCGBZAthFziGAXVClTAhAAAIQgECHBBBABNCaXgiglSDxEIAABCAAgcAEEEAE0JpyCKCVIPEQgAAEIACBwAQQQATQmnIIoJUg8RCAAAQgAIHABBBABNCacgiglSDxEIAABCAAgcAEEEAE0JpyCKCVIPEQgAAEIACBwAQQQATQmnIIYA2C29un9c1vntBdd23pHveY0aWXzmtqyr2YhQ8EIAABCEAgPAEEEAG0Zh0COIHg7bcf08mTy/rudzfOHXnRRbO66qrDuve9F638iYcABCAAAQg0JoAAIoCNk2YkAAHcg6CTv89+dql6BfPwgVNn/vIjP7LauwSePn1aJ06c0NbWlmZmZjQ/P6/paWYnrQODeAhAAAIxE0AAEUBrfiKAuxB0t30/+tH9F8z8XXjolNxM4KMfvd7b7eBjx45peXlZGxvnZydnZ2d1+PBhLS4yO2kdHMRDAAIQiJUAAogAWnMTAdyF4H/913F9+tMHJvJ9+MPXdNllCxOP832Ak7+lpSVtb29fUPTU1NnZydXVVSTQN3TKgwAEIBAJAQQQAbSmIgK4C8Hbbjuqz3/+0ES+D3rQEd3nPu51zOE+7rbv/v37L5j5Gz67k0A3E7i+vs7t4HDdwpkgAAEIBCOAACKA1mRDABOcATx+/LgOHJg8O7m2tqaFhfCzk9akJB4CEIAABPYmgAAigNYxggDuQvD8GsDNMQ+BuKD+1gAePXpUhw5Nnp08cuSIDh4MOztpTUjiIQABCEBgMgEEEAGcnCV7H4EA7sHn/FPA7qDhtXb9PgXMDKA17YmHAAQgkDYBBBABtGYwAjiB4Ph9AOd01VUr3raAabqVy2AN4Obm5o6HQM7MTbIG0DouiIcABCAQNQEEEAG0JigCWINgl28CabuVy+Ap4DNzk0NPAvMUcI0O5RAIQAACiRNAABFAawojgFaChnjrVi7j5HFubk4rKytsAWPoF0IhAAEIxE4AAUQArTmKAFoJtoz3tZVL09vHLatLGAQgAAEIREQAAUQAremIAFoJtozv8kEOpLBlpxAGAQhAIBECCCACaE1VBNBKsGV8V1u5tF1T2LIZhEEAAhCAQA8EEEAE0Jp2CKCVYMv4LmYArWsKWzaFMAhAAAIQCEwAAUQArSmHAFoJtoz3vZWLrzWFLZtDGAQgAAEIBCSAACKA1nRDAK0EDfE+t3LpYkbR0DRCIQABCECgQwIIIAJoTS8E0ErQGO9rK5eu1hQam0c4BCAAAQh0QAABRACtaYUAWgl6iPfx1C4zgB46giIgAAEIJEIAAUQAramKAFoJRhLve01hJM2iGhDYQcDHDyawQiB1AgggAmjNYQTQSjCieJ9rCiNqFlWBwDkCbHNEMkDgLAEEEAG0jgUE0EowsnhfawojaxbVgYDY5ogkgMB5AgggAmgdDwiglWCE8dwii7BTqJKJANscmfARnCEBBBABtKY1AmglSDwEINA5AR5y6hwxJ0iMAAKIAFpTFgG0EiQeAhDonADbHHWOmBMkRgABRACtKYsAWgkSDwEIdE6AGcDOEXOCxAgggAigNWURQCtB4iEAgc4JsM1R54g5QWIEEEAE0JqySQmg5eEGS6wVMvEQgICdANsc2RlSQj4EEEAE0JrNyQigZf8vS6wVMPEQgIA/Amxz5I8lJaVNAAFEAK0ZnIQAWvb/ssRa4RIPAQj4J8Bsvn+mlJgeAQQQAbRmbfQCaNn/yxJrBUt8NwT48u+GK6V2R4Cc7Y5tySUjgAigNf+jF0DL03+WWCtY4v0T4Fa+f6aU2C0BcrZbviWXjgAigNb8j14ALft/WWKtYIn3S4Bb+X55Ulr3BMjZ7hmXfAYEEAG05n/0AmiZxbPEWsES748At/L9saSkMATI2TCcSz4LAogAWvM/egG07P9libWCJd4fgRJEnnVi/vIlhpJKyNkYOJdcBwQQAbTmf/QC6Bpo2f/LEmuFS7wfArnfymedmJ88iamU3HM2Jtal1gUBRACtuZ+EAA4kcHl5WRsbG+faPDc3p5WVFS0uLu7Jgb3DrGnSb3zOsymsE+s3t7o6e8452xUzym1GAAFEAJtlzM6jkxFAV3XLbTJLrBUy8TYCud7KZ52YLS9ijs41Z2NmXlrdEEAE0JrzSQmgtbHEp0sg1Vv5e/3wYJYo3XysU/NUc7ZO2zimfwIIIAJozUIE0EqQ+GAEUruVP2ltH+vEgqVObydKLWd7A8WJGxNAABHAxkkzEoAAWgkSH5RAKrfy66ztu/zyy3XgwIGJ/NbW1rSwsDDxOA6Ik0AqORsnPWq1GwEEEAG0jg4E0EqQeAiMEKi7tu/kyZO68sortbm5qe3t7R0cp6amNDs7q/X1dU1PT8MZAhCAwDkCCCACaB0OCKCVIPEQGCHQZG3fHXfcoaWlpTMlDEugkz/3WV1dnfiUOx0AAQiURwABRACtWY8AWgkSD4ERAk3X9rFOjBSCAASaEkAAEcCmOTN6PAJoJUg8BAwzgIO1fawTI40gAIEmBBBABLBJvow7FgG0EiQeAiME2AOOlIAABLomgAAigNYcQwCtBImHwBgC7AFHWkAAAl0SQAARQGt+IYBWgsRDYBcCrO0jNSAAga4IIIAIoDW3EEArQeIhsAcB1vaRHhCAQBcEEEAE0JpXCKCVYMN4hKAhMA6HAAQgAIEdBBBABNA6LBBAK8EG8ZNeDdagKA6FAAQgAIGCCSCACKA1/RFAK8Ga8XVeDba4uFizNA6DAAQgAIGSCSCACKA1/xFAK8Ea8XVfDcYrv2rA5BAIQAACEBACiABahwECaCVYI77Jq8EGGwPXKHbXQ1hnaKFHLAQgAIH2BEJdfxFABLB9lp6NRACtBGvEN301WI0idz2EdYYWesRCAAIQaE8g5PUXAUQA22cqAmhlVzs+1Awg6wxrdwkHQgACEPBKIPT1FwFEAK0JzAyglWCN+DavBmt6G4F1hjU6gkMgAAEIdECgj+svApi3AL5Kknss9IGSvi3pnyS9QtIXhvL3npLeIulZki6S9AFJL5Z0W80cRwBrgrIe1uTVYG1uI4SaZbRyIB4CEIBAbgT6uP4igHkL4PslvUfSxyTdXdIbJT1E0oMl/W81gN4h6amSrpF0StINkr4n6bE1BxgCWBOUj8PqvBqs7W2EkOsMfbCgDAhAAAK5EOjj+osA5i2Ao2Pj3pK+Ienxkv5R0iWSbpd0SNJqdbCbLfy8pMdI+miNwYUA1oDk85C9bu1abiP08QvUJxfKggAEIJAqgT6uvwhgWQJ4laQvSXqopH+T9FOSPijpMknfHBo4X5W0Iun6MYPJ3SZ2fwafiyVtnDp1Svv2ORfk0ycBy0WkzTrDPtvKuSEAAQjkQqCP6y8CWI4A3k3SX0u6VNJPVoPGzfzdOCJ07p/+RdJatV5wdHy9VtJ1o/8RAYzjMmS9jdBknWEcLaYWEIAABPIgEPr6iwCWI4Burd+TK/nbmCCAbs2gmxl8JTOAaV1YLDOAg5bWWWeYFhVqCwEIQCANAiGvvwhgGQLoHuz4eUmPk7Q+NAza3AIeHUWsAYzouuLrNkLTLWQiQkBVIAABCCRNINT1FwHMWwCnJL1N0tMkLVTr/4YHxuAhkIOSbqr+4f7VNjE8BJLoJST0bYREMVFtCEAAAkUTQADzFsC3V0/4utm/4b3/3HYvbl9A93G3hp9SbQNzZyWM7r9fXXNkMANYE1TIw0LeRgjZLs4FAQhAAAJ+CCCAeQvg9i5p8lxJ76z+bbARtJsFHN4I+us1UwwBrAkq9GGhbiOEbhfngwAEIAABOwEEMG8BtGfI5BIQwMmMOAICEIAABCAQFQEEEAG0JiQCaCVIPAQgAAEIQCAwAQQQAbSmHAJoJUg8BCAAAQhAIDABBBABtKYcAmglSDwEIAABCEAgMAEEEAG0plynAsiDDNbuIR4CEIAABCCwkwACiABax0VnAjhuK5PZ2VkdPnxYi4uL1noTDwEIQAACECiWAAKIAFqTvxMBHGxmvL194U42U1Nub2tpdXUVCbT2HPEQgAAEIFAsAQQQAbQmv3cBHLzObGNj8MriC6voJNDNBK6vr2t6etpaf+IhAAEIQAACxRFAABFAa9J7F8Djx4/rwIEDE+u1tramhQX3hjs+EIAABCAAAQg0IYAAIoBN8mXcsd4F8OjRozp06NDEeh05ckQHD7oXmPCBAAQgAAEIQKAJAQQQAWySL0EEkBlAa5cQDwEIQAACENibAAKIAFrHiPcZwMEawM3NTY0+BOIqW9IaQLbBsaYn8RCAAATSJ9DFdwECiABaR4Z3AXQVGjwF7P7/sASW9BQw2+BYU5N4CEAAAukT6Oq7AAFEAK2joxMBHEjg8vKyhp8Gnpub08rKSvZbwLANjjUtiU+VwOnvndaJr53Q1n9vaebiGc3/n3lN342n/VPtT+ptI9DldwECiADaslPqTABdxbqY9rY2uOt4tsHpmjDlx0rg2OePafn9y9q48/wWULP7ZnX4SYe1+CA2f4+136hXNwS6/i5AABFAa+Z2KoB1K5eTKPIQTN1e57icCDj5W3rvkrY1svm7qs3fn7GKBObU4bRlIoGuvwsQQARwYhJOOKB3AexqfYQVTNt4tsFpS464VAm42777D++/YOZvuC1TmpKbCVxfXud2cKqdTL0bE+j6uwABRAAbJ+VIQK8C2OX6CCuYtvFd/+prWy/iINAVgeP/cVwH3lVj8/fnrGlhP5u/d9UPlBsXga6/CxBABNCa8b0JYNfrI6xg2sazDU5bcsSlSuDoZ47q0LEam78vHtHBh7L5e6r9TL2bEej6uwABRACbZeTOo3sTwK5/HVnBWOLZBsdCr5vYnNaZdkOofanMALZnR2TeBLr8LkAAEUDr6OlNALteH2EFY40ft7axlG1wrOx8x+e2ztQ3H2t5gzWAm3du7ngIxJXNGkArYeJTJtDVdwECiABax0VvApjzDOCgU5h1sqanPT7HdaZ2Kv5LGDwF7EoefhLYyZ/7rPIUsH/olJgMgS6+CxBABNA6AHoTwK7XR1jBEJ8+gVzXmcbaM+P2AZzbN6eVJ62wBUysnUa9kiWAACKA1uTtTQBdxbtcH2EFQ3z6BEqYZY6tl3gTSGw9Qn1yJYAAIoDW3O5VAAcSWOor46ydR/zeBHJfZ0r/QwAC5RJAABFAa/b3LoCuAV2sj7CCIT59AswApt+HtAACEBhPAAFEAK1jIwoBtDaCeAiMIxB6nSk/ZMhDCEAgFAEEEAG05hoCaCVIfNQEQq0zZauZqNOAykEgOwIIIAJoTWoE0EqQ+OgJdLUP16DhbDUTfQpQQQhkRwABRACtSY0AWgkSnwSBrm7PstVMEt1PJSGQHQEEEAG0JjUCaCVIfNEEUn/QpCsxLjopaDwEAhBAABFAa5ohgFaCxBdNIOWtZli3WHTq0vjECSCACKA1hRFAK0HiiyaQ6gwg6xaLTlsanwEBBBABtKYxAmglSHzRBEJvNeMDNusWfVCkDAj0SwABRACtGYgAtiDIuqkW0DIOCbXVjC+Eqc5a+mq/r3Jiug7EVBdffClnbwIIIAJoHSMIYEOCrJtqCKyQw7veasYnxpTXLfrkYCkrputATHWxMCW2GQEEEAFsljE7j0YAGxBk3VQDWAUemsosDDOAtuSM6ToQU11sVIluSgABRACb5szo8QhgTYKsm6oJqpDDUpG9cd2R4rrFWNIqputATHWJpX9KqgcCiABa8x0BrEmQWZOaoAo4LIdbbqmtW4wlrWK6DsRUl1j6p6R6IIAIoDXfEcCaBFk3VRNU5ofldMstpXWLsaRVTNeBmOoSS/+UVA8EEAG05jsCWJMgv7Zrgsr4sBxvuaV8K7uPVIvpOhBTXfroi9LPiQAigNYxgADWJMi6qZqgMj6ML9yMO7dm02K6DsRUl5r4OMwjAQQQAbSmEwLYgCDrphrAyvBQbrll2KktmhTTdSCmurRASYiBAAKIABrS50woAtiQIOumGgLL6HBmADPqTGNTYroOxFQXI1bCGxBAABHABuky9lAEsAVB1k21gJZBCLfcMuhEj02I6ToQU108IqaoPQgggAigdYAggFaCxBdFgFtuRXU3jYVAtAQQQATQmpwIoJUg8cUR4JZbcV1OgyEQHQEEEAG0JiUCaCVIfJEEuOVWZLfTaAhEQwABRACtyYgAWgkSD4GABBDPgLA5FQQiJoAAIoDW9EQArQSJh0AgAjm8gi4QKk4DgewJIIAIoDXJEUArQeIhEIBATq+gC4CLU0AgewIIIAJoTXIE0EqQeAh0TCDHV9B1jIziIZA9AQQQAbQmOQJoJZhZfC5rzHJph0svNqDObJDRHAh4IIAAIoDWNEIArQQzis9ljVku7RikFq+gy2iQ0RQIeCKAACKA1lRCAK0EM4nPZY1ZLu0YTitmADMZZDQDAh4JIIAIoDWdEEArwQzic1ljlks7RlOKV9BlMMhoAgQ8E0AAEUBrSiGAVoIZxOcyw5RLO8alFK+gS2Og5bT2dNwPkRMnTmhra0szMzOan5/X9PR0Gh2TYS0RQATQmtYIoJVgBvG5rDHLpR27pRSvoIt7sOW29nSYds5tizurdq8dAogAWnMXAbQSzCA+l5mzXNqxV0rlPMOU8lDKce3poD9yblvKOYcAIoDW/EUArQQziM9ljVku7cggpYpqQq5rT10n5ty21JMUAUQArTkcrQAy02Ht2mbxuawx66Id5GKzXIrh6JB9lvPMc85tiyFPLXVAABFAS/642CgFkPUm1m5tF5/LGjOf7SAX2+VSn1Gh+yzntac5t63PHPVxbgQQAbTmUXQCyHoTa5fa4kPOnNhqune0j3aQi132UDdl99FnOc+S5dy2bjIwXKkIIAJozbaoBJD1JtbuJN4XAXLRF8lw5fTVZzmvPc25beEys5szIYAIoMusX5P0ckk/KOnTkn5d0r/UTLmoBJBfmzV7jcM6J0Audo7Y+wn67LMu1p56B9SywJzb1hJJFGEIIAL4TEnvlvRCSf9P0m9KerqkB0j6Ro0sjUoAWW9So8c4JAgBcjEIZq8n6bvPfK499QrGQ2E5t80Dnl6KQAARQCd9H5P0kioD7ybpFklvk/SmGlkZlQD2+Qu+BisOKYgAuZheZ8fQZz7WnsZKPue2xcp8r3ohgGUL4D0kfUvSkqS/GkqUd0m6VNLPj0meiyS5P4PPxZI2brnlFu3b51yw34+7wDzkIQ/RrbfeumtF7nvf++ozn/kMryDqt6uyPzu5mF4X02fp9Rk1bk/ACeDc3Jwr4BJJd7YvKd3IqXSrbq75FZI2JV0t6Z+HSvt9SY+X9KgxZ3itpOvMZ6YACEAAAhCAAARiIPB/Jf1HDBUJXQcEcKcA/oGkeUmPHtMZY2cAJc1K+u/Qncf5LiBwZjaWvogiK+iLKLrhXCXoj3j6g76Iry+YAYynT4LVpM0t4NHKnVkDWPIUcrDemnwi+mIyo1BH0BehSNc7D/1Rj1OIo+iLEJTrnaP4vih5BtCliHsIxG354rZ+cR/3pPtE3AAACYVJREFUEMjXJN3Q5CEQBLDeaOv4qOIHc8d8mxRPXzSh1f2x9Ef3jOuegb6oS6r744rvi9IFcLANzPMrEXTbwDxD0gMl3VYj/4pPoBqMQh1CX4QiPfk89MVkRiGPoD9C0t77XPQFfRENgdIF0HWE2wJmsBH0pyT9RjUzWKeT3JrAV0n6XUnfrRPAMZ0RoC86Q9u4YPqiMbJOA+iPTvE2Kpy+aISr04OL7wsEsNP8onAIQAACEIAABCAQHwEEML4+oUYQgAAEIAABCECgUwIIYKd4KRwCEIAABCAAAQjERwABjK9PqBEEIAABCEAAAhDolAAC2CleCocABCAAAQhAAALxEUAA2/fJrw09Pfzpai9Bt6cgn+4IuCeuF6tter4t6Z8kvULSF4ZOeU9Jb5H0rOq9zR+Q9OKa2/p0V/P8S3Z980ZJhyW57ZTch74I2+/3lfR7kp4s6V6STkp6rqSPV9Vw1/vXSXpe9b7zj0h6kaQvha1m9mebluReG/pLkn5Qkns5+zslvUHSNn3Raf8/rvpe/jFJM5KeJumvhs5YZwxcLultkn5O0vck3SRpWdL/dFrzHgpHANtBH+wf+MJqyxj3hfd0SQ+Q9I12RRJVg8D7Jb1H0sck3b0SjodIerCk/63i3yHpqZKuqd7S4jb1doP4sTXK55B2BB4p6b3VC9XXhgSQvmjHs03UZZI+Kcnxd9xvl/TDkr5c/XFluh9LTtTd2PiKpNdLemg1fr7T5qTEjCXwakkvk/QcSZ+V9OOSbpT0GklvrSLoi26Sx/34cdf6T1TiNiqAdbj/XSWPL5D0fVXfue+cQ91Uub9SEcB27N0bRFxCuD0E3ce9QeSW6lfDm9oVSVQLAveuhPvxkv6xeiOL++JzA3W1Ks9t6v15SY+R9NEW5yBkbwLfX11s3SzrtZLcXpruB5F7vyZ9ES573HXHffG595iP+7hrvZuJcrPjb64OcH3kNrx3Quh+WPHxQ+BvKq6/MlScm0Vydy3crCB94YfzpFLcbOuwANbh/iBJn5PkftQOZs6fJOlvq/fMuzGUzQcBbN6VPt4h3PysRIwjcFV1+8rNYvybpJ+S9EFJbjbkm0MBX5W0Iul6MHon8C5Jd0h6qaTjQwJIX3hHvWeB7kvLLXeYleR+EG1KerukP62i7lfNBD6i6qNBYR+q/u5ucfHxQ8DNALq3Sz1R0hclPVzS31ezgn8hib7ww3lSKaMCWIf7L1c/ktx3yODj7ja5GXJ3l+8vJ500pX9HAJv31hXVxfVqSf88FP771YX3Uc2LJKIFATfr+tfVWqafrOLdzJ+71eJ2eB/+uLWZ7taYm/7n44+AW2fpbmu5X8vuAjksgPSFP851Shrcwv1DSe+T9BPVjx53G+vdktz1yq35c9evraEC3a1790XplrXw8UPAXZvcetjfknRaklsT6MaJe2OU+9AXfjhPKmVUAOtwd/Lubt275VzDH7e067pqecWk8ybz7whg867aTQD/oLr98ujmRRLRgoBb5+TWezj526jid5MOd7vezQy+ssV5CBlPYK66ReJmOdxDUO5TRwDpi24y6q6qP9yX3ODj1ps5OXfLH3b78nOy6CTFyTwfPwQcS/d94F4x6tYA/mgl425doJsxpy/8cJ5USl0BHB4DuwmgW87y25L+eNJJU/p3BLB5b3ELuDkz3xHuwY6fl+Se+FofKpzbjr5J717eL1S3Q5w8DD5upsNddN1DNz8j6WZuxwfrELfM4R8k/erQGd0Tvm5dpns6uM7tr2CVzfxEbj24W5P5R0PtdP3g1v+5Ncn0RZgE4BbwBM4IYLtEdA+BuNuKv16Fuyn/r0lyYsJDIO2Y1oly+eoez3cLexfGbF8xePDgYPUEmCvz/tU2MTwEUodw/WMulvRDI4e72+//Xm1F4r4E3a9m+qI+U8uRRyS5Wdnhh0Dcmle3JMXNOA0WwLsHQNyDIO6zr3qIiodALOR3xv5nJd7uLsXg456+dlvyuOsRfeGX926l7fYQyF5jYPAQiHty+1+rgt1dDrcDhVtfy0MgYfou6rMMtoFxC32dCLqnHp9R/bpzT9Xx6YaAW9TubvO62b/hvf9OVU/YubO6i+5Tqicb76yE0f334Vtj3dSOUodvAdMXYfPB3ep1+2K6dUpuXZ9bA+geAHHXKPfggfu4NbBuGYRb4+Rmzt02MA9jGxjvHeX2/HuCJLf+0t0Cdg/e/ImkPxtah0xfeMd+pkC3K4F7ONB93LZI7ra7W//tHlRzkzR1uLttYO4jyW3zNtgGxj0RzDYw3fRZkqW6LWDcGg+30afb+uI3qj0Bk2xMIpUebKI6Wl33y9pddN1nsPmwm3lyD4MMNoL+eiJtTLmaowJIX4TtzZ+tHjRw+/85wXMPhAyeAnY1GWyC66TwUkkfrjZJd0+q8vFHwM2OO7l2dyp+oJo1OirpdyS5tZr0hT/WoyW5O0NO+EY/bu2lm+muMwbcRtDubt7wRtDu+52NoLvrN0qGAAQgAAEIQAACEAhBgDWAIShzDghAAAIQgAAEIBARAQQwos6gKhCAAAQgAAEIQCAEAQQwBGXOAQEIQAACEIAABCIigABG1BlUBQIQgAAEIAABCIQggACGoMw5IAABCEAAAhCAQEQEEMCIOoOqQAACEIAABCAAgRAEEMAQlDkHBCAAAQhAAAIQiIgAAhhRZ1AVCEAAAhCAAAQgEIIAAhiCMueAAAQgAAEIQAACERFAACPqDKoCAQhAAAIQgAAEQhBAAENQ5hwQgAAEIAABCEAgIgIIYESdQVUgAAEIQAACEIBACAIIYAjKnAMCEIAABCAAAQhERAABjKgzqAoEIAABCEAAAhAIQQABDEGZc0AAAhCAAAQgAIGICCCAEXUGVYEABCAAAQhAAAIhCCCAIShzDghAAAIQgAAEIBARAQQwos6gKhCAAAQgAAEIQCAEAQQwBGXOAQEIQAACEIAABCIigABG1BlUBQIQgAAEIAABCIQggACGoMw5IAABCEAAAhCAQEQEEMCIOoOqQAACEIAABCAAgRAEEMAQlDkHBCAAAQhAAAIQiIgAAhhRZ1AVCEAAAhCAAAQgEIIAAhiCMueAAAQgAAEIQAACERFAACPqDKoCAQhAAAIQgAAEQhBAAENQ5hwQgAAEIAABCEAgIgIIYESdQVUgAAEIQAACEIBACAIIYAjKnAMCEIAABCAAAQhERAABjKgzqAoEIAABCEAAAhAIQQABDEGZc0AAAhCAAAQgAIGICPx/dNO2z1Gu3fkAAAAASUVORK5CYII=\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(0, 100)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "for i in range(1000):\n",
    "    centroids_best_fit_point = [\n",
    "\n",
    "    ]\n",
    "    for i in range(centroids_count):\n",
    "        centroids_best_fit_point.append([])\n",
    "    # closest centroid from data point\n",
    "    for i in range(data_points_count):\n",
    "        best_fit_index = 0\n",
    "        best_fit_distance = 0\n",
    "        for centroid_index in range(len(centroids_position)):\n",
    "            centroid = centroids_position[centroid_index]\n",
    "            distance = euclidian_distance([data_points[\"x\"][i], data_points[\"y\"][i]], centroid)\n",
    "            if(centroid_index == 0 or distance <= best_fit_distance):\n",
    "                best_fit_index = centroid_index\n",
    "                best_fit_distance = distance\n",
    "        centroids_best_fit_point[best_fit_index].append([data_points[\"x\"][i], data_points[\"y\"][i]])\n",
    "\n",
    "    for i in range(centroids_count):\n",
    "        mean_x = 0\n",
    "        mean_y = 0\n",
    "        test = []\n",
    "        for j in range(len(centroids_best_fit_point[i])):\n",
    "            mean_x += centroids_best_fit_point[i][j][0]\n",
    "            mean_y += centroids_best_fit_point[i][j][1]\n",
    "            test.append(centroids_best_fit_point[i])\n",
    "\n",
    "        mean_x /= len(centroids_best_fit_point[i]) + 1\n",
    "        mean_y /= len(centroids_best_fit_point[i]) + 1\n",
    "        \n",
    "        centroids[\"x\"][i] = mean_x\n",
    "        centroids[\"y\"][i] = mean_y\n",
    "        \n",
    "        centroids_position[i][0] = mean_x\n",
    "        centroids_position[i][1] = mean_y \n",
    "        \n",
    "#print(centroids)\n",
    "for i in range(centroids_count):\n",
    "    plt.scatter(centroids[\"x\"][i], centroids[\"y\"][i], color=colors[i])\n",
    "\n",
    "plt.scatter(data_points['x'], data_points['y'], color='k')\n",
    "plt.xlim(0, 100)\n",
    "plt.ylim(0, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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